A pool rack is an equilateral triangle, filled with 15 equal-sized balls. Seen from above, we'd see a triangle, with 15 circles within.

Imagine we used smaller and smaller balls. The more the balls, more area of the triangle would be covered.

In the limit, with infinite balls, would all of the triangle be covered?

(In reply to re: Solution by Richard)

I believe he got it using the formula A=(s^2)(sqrt(3))/4 for the area of an equilateral triangle with side length s.  It's pretty basic to get the formula he described with that.

Posted by David Shin on 2004-09-24 01:41:32